Botham, the grandson of former England cricket all-rounder Ian, sparked Wales' remarkable comeback against Scotland in his first test in almost three years in Cardiff on Saturday.
He barged over for the side's first try as they scored 26 unanswered points but fell agonisingly short in a thrilling 27-26 defeat.
The length of his absence is unknown, with Welsh Rugby confirming he will return to his club Cardiff to continue his rehabilitation.
Davies has been called to cover the back row having trained with the team last week, though he was not officially a part of the squad then.
Lewis comes into contention after Leon Brown went off at half-time against the Scots with a knock, though the latter remains with the team for now.
Wales do have two other tightheads in Keiron Assiratti, who has three international appearances, and uncapped Archie Griffin. Lewis is a veteran of 54 caps and adds experience in that position.
The youthful selection are seeking a first win against England at Twickenham since the 2015 Rugby World Cup, and a first Six Nations success in London for 12 years.
Coach Warren Gatland will name his team on Thursday.